Shear Force Diagram (SFD) Calculator
Calculate internal transverse shear forces along any beam span. Identify point load jump discontinuities, support reactions, and locate zero-shear crossings.
dV(x)/dx = -w(x) ⟹ V(x) = V₀ - ∫ w(x) dx
Beam Master handles any combination of point loads, uniform distributed loads (UDL), varying loads (UVL), and applied moments with instant SFD, BMD, and deflection curves.
How Shear Force Curves Behave
The internal shear force $V(x)$ represents the total algebraic sum of vertical forces acting on one side of a cut section. Under no distributed load, $V(x)$ remains strictly horizontal (constant). Under a uniform load $w$, it slopes downward linearly.
Engineering Formulas & Governing Equations
Shear-Load Differential Equation
Equation 01The rate of change (slope) of the shear diagram equals the negative distributed load intensity.
Concentrated Point Load Discontinuity (Jump)
Equation 02A downward point load causes an abrupt step drop equal to the force magnitude P in the SFD.
Support Upward Reaction Jump
Equation 03An upward reaction force causes an instant vertical step rise equal to reaction R.
Uniform Distributed Load (UDL) Slope
Equation 04A uniform load creates a constant downward sloping linear shear force curve with slope -w.
Calculation Details & Clarifications
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